You're missing a couple of data points. 1806 The United States Congress passed the Act Prohibiting Importation of Slaves, which took effect January 1st, 1808. The 1807 law the British Parliament passed didn't take effect until March 1808. 1808 was also the soonest the United States Congress was able to ban the importation of Slaves under Article I Section 9 of the Constitution. In effect, the British Empire stopped trading slaves when its largest market for slaves stopped importing them. Just to round this out, while you are partially right because Brazil at this time was not its own nation, it was later than the United States in abolishing slavery by about 23 years, 1888.
You missed the point of my post though: the difference between slavery today and slavery in the 18th Century is whether it is state sanctioned or not. There is an extant global slave trade that is larger than the Trans-Atlantic Slave Trade at its peak, but now it is a mostly black market trade.
The 13th Amendment has a flaw as well; it allows for prison slavery.
> Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
The Black Codes passed within the Antebellum South made full use of this qualifier to essentially criminalize Blackness and re-enslave Freedmen through the prison system.
I'm not saying it was just, nor am I denying the hypocrisy present within the Constitution at the time of its ratification which is in direct contradiction to the spirit of the Declaration of Independence. That said, there is such a thing as voluntary slavery, and debt bondage. The former was a means of providing for yourself or your child and is a practice that was recorded as far back as the Code of Hammurabi. The latter has a history in the Americas, Asia, Europe and Africa, and is still widespread in South Asia and Subsaharan Africa. Voluntary slavery is a liberty, but because the 13th Amendment does not make any kind of distinction, it is prohibited along with all other forms except prison slavery, hence my characterization of the 13th as a prohibition article.
You can fault the United States for being one of the last countries to (mostly) abolish slavery if you like. That's fine, but it's not the criticism I would levy, there's plenty of Reconstruction Era and post-Reconstruction Era problems stemming from how poorly the Lincoln Amendments were written which were written with the best of intentions, badly. There's also the fact that the Emancipation Proclamation was in 1862 and the 13th Amendment was passed in 1865 just prior to the end of the Civil War. It's now been 155 years, and the 13th Amendment has been in force over twice as long as all of the clauses related to slavery in the Constitution.
In the absence of law though, there is often slavery. Peoples who are weaker than their neighbors and have nothing else to offer are usually enslaved by their neighbors. If you don't have greater martial power and it isn't costly to take you, you're dead, or a slave.